COMBINANDO AS TÉCNICAS DE BUSCA LINEAR COM CONTINUAÇÃO PARA A SOLUÇÃO DE PROBLEMAS ESTRUTURAIS NÃO LINEARES

Resumo

The demand for computational tools that simulate the real behavior of structures has been
intensified. Such numerical simulations usually involve highly nonlinear problems. For nonlinear
static problems, in particular, it is fundamental the implementation and use of numerical strategies to
trace the structure equilibrium paths in a complete way, overcoming critical points (limit and
bifurcations points). In the Finite Element Method (FEM) context, where incremental-iterative
strategies are usually adopted, the nonlinear solvers must have a high level of efficiency in the two
phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear
algebraic equations, it is quite common that Newton-Raphson's iterations do not converge or require
an excessive number of iterations near the critical points. Therefore, the linear search optimization
technique appears as an additional sophistication. Basically, this technique aims to stagger the
corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the
convergence of the process. The purpose of this work is to verify the efficiency of linear search
technique coupled with Newton-Raphson iterations and different path-following methods, and verify
its influence on the nonlinear solver efficiency. The effectiveness of the linear search algorithm
implemented is verified in solving slender structures with accentuated nonlinearity. It is previously
perceived that such a resource is triggered near load limit points (with more success when applied to
structures with these critical points), accelerates the iterative process and increases the chances of
convergence.